Thesis (Ph. D.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2006. / Dr. Alfred Andrew, Committee Member ; Dr. Ye (Geofferey) Li, Committee Member ; Dr. Nikil S. Jayant, Committee Member ; Dr. Gordon L. Stuber, Committee Chair ; Dr. Douglas B. Williams, Committee Member Vita. Includes bibliographical references.

This thesis presents algorithms for performing the next two reduction steps, namely orthogonalization and extraction. More specifically, this thesis addresses the following research question: What are proper methods of orthogonalizing spectral images in preparation for extraction?

Abstract not available

The general objective of this proposed research is to design and develop signal acquisition and tracking algorithms for multiple input multiple output orthogonal frequency division multiplexing (MIMO-OFDM) systems for fixed wireless access applications. The algorithms are specifically targeted for systems that work in time division multiple access and frequency division multiple access frame modes. In our research, we first develop a comprehensive system model for a MIMO-OFDM system under the influence of the radio frequency (RF) oscillator frequency offset, sampling frequency (SF) offset, RF oscillator phase noise, frequency selective channel impairments and finally the additive white Gaussian noise. We then develop the acquisition and tracking algorithms to estimate and track all these parameters. The acquisition and tracking algorithms are assisted by a preamble consisting of one or more training sequences and pilot symbol matrices. Along with the signal acquisition and tracking algorithms, we also consider design of the MIMO-OFDM preamble and pilot signals that enable the suggested algorithms to work efficiently. Signal acquisition as defined in our research consists of time and RF synchronization, SF offset estimation and correction, phase noise estimation and correction and finally channel estimation. Signal tracking consists of RF, SF, phase noise and channel tracking. Time synchronization, RF oscillator frequency offset, SF oscillator frequency offset, phase noise and channel estimation and tracking are all research topics by themselves. A large number of studies have addressed these issues, but usually individually and for single-input single-output (SISO) OFDM systems. In the proposed research we present a complete suite of signal acquisition and tracking algorithms for MIMO-OFDM systems along with Cramr-Rao bounds for the SISO-OFDM case. In addition, we also derive the Maximum Likelihood (ML) estimates of the parameters for the SISO-OFDM case. Our proposed research is unique from the existing literature in that it presents a complete receiver implementation for MIMO-OFDM systems and accounts for the cumulative effects of all possible acquisition and tracking errors on the bit error rate (BER) performance. The suggested algorithms and the pilot/training schemes may be applied to any MIMO OFDM system and are independent of the space-time coding techniques that are employed.

Wireless devices in wireless networks are powered typically by small batteries that are not replaceable nor recharged in a convenient way. To prolong the operating lifetime of networks, energy efficiency is indicated as a critical issue and energy-efficient resource allocation designs have been extensively developed. We investigated energy-efficient schemes that prolong network operating lifetime in wireless sensor networks and in wireless relay networks. In Chapter 2, the energy-efficient resource allocation that minimizes a general cost function of average user powers for small- or medium-scale wireless sensor networks, where the simple time-division multiple-access (TDMA) is adopted as the multiple access scheme. A class of Ç-fair cost-functions is derived to balance the tradeoff between efficiency and fairness in energy-efficient designs. Based on such cost functions, optimal channel-adaptive resource allocation schemes are developed for both single-hop and multi-hop TDMA sensor networks. In Chapter 3, optimal power control methods to balance the tradeoff between energy efficiency and fairness for wireless cooperative networks are developed. It is important to maximize power efficiency by minimizing power consumption for a given quality of service, such as the data rate; it is also equally important to evenly or fairly distribute power consumption to all nodes to maximize the network life. The optimal power control policy proposed is derived in a quasi-closed form by solving a convex optimization problem with a properly chosen cost-function. To further optimize a wireless relay network performance, an orthogonal frequency division multiplexing (OFDM) based multi-user wireless relay network is considered in Chapter 4. / In the OFDM approach, each subcarrier is dynamically assigned to a source- destination link, and several relays assist communication between pairs of source-destination over their assigned subcarriers. Using a class of Ç-fair cost-functions to balance the tradeoff between energy efficiency and fairness, jointly with optimal subcarrier and power allocation schemes at the relays. Relevant algorithms are derived in quasi-closed form. Lastly, the proposed energy-efficient schemes are summarized and future work is discussed in Chapter 5. / by Di Wang. / Thesis (Ph.D.)--Florida Atlantic University, 2011. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2011. Mode of access: World Wide Web.

The three-body bound state problem is considered using configuration-space Faddeev equations within the framework of the total-angular-momentum representation. Different three-body systems are considered, the main concern of the investigation being the i) calculation of binding energies for weakly bounded trimers, ii) handling of systems with a plethora of states, iii) importance of three-body forces in trimers, and iv) the development of a numerical technique for reliably handling three-dimensional integrodifferential equations. In this respect we considered the three-body nuclear problem, the 4He trimer, and the Ozone (16 0 3 3) system. In practice, we solve the three-dimensional equations using the orthogonal collocation method with triquintic Hermite splines. The resulting eigenvalue equation is handled using the explicitly Restarted Arnoldi Method in conjunction with the Chebyshev polynomials to improve convergence. To further facilitate convergence, the grid knots are distributed quadratically, such that there are more grid points in regions where the potential is stronger. The so-called tensor-trick technique is also employed to handle the large matrices involved. The computation of the many and dense states for the Ozone case is best implemented using the global minimization program PANMIN based on the well known MERLIN optimization program. Stable results comparable to those of other methods were obtained for both nucleonic and molecular systems considered. / Physics / D.Phil. (Physics)

The three-body bound state problem is considered using configuration-space Faddeev equations within the framework of the total-angular-momentum representation. Different three-body systems are considered, the main concern of the investigation being the i) calculation of binding energies for weakly bounded trimers, ii) handling of systems with a plethora of states, iii) importance of three-body forces in trimers, and iv) the development of a numerical technique for reliably handling three-dimensional integrodifferential equations. In this respect we considered the three-body nuclear problem, the 4He trimer, and the Ozone (16 0 3 3) system. In practice, we solve the three-dimensional equations using the orthogonal collocation method with triquintic Hermite splines. The resulting eigenvalue equation is handled using the explicitly Restarted Arnoldi Method in conjunction with the Chebyshev polynomials to improve convergence. To further facilitate convergence, the grid knots are distributed quadratically, such that there are more grid points in regions where the potential is stronger. The so-called tensor-trick technique is also employed to handle the large matrices involved. The computation of the many and dense states for the Ozone case is best implemented using the global minimization program PANMIN based on the well known MERLIN optimization program. Stable results comparable to those of other methods were obtained for both nucleonic and molecular systems considered. / Physics / D.Phil. (Physics)

This thesis describes a genetic approach for shaping the dynamic responses of linear state space systems through pole placement. This paper makes further comparisons between this approach and an island approach parallel genetic algorithm (PGA) which incorporates orthogonal mutation vectors to increase sub-population specialization and decrease convergence time. Both approaches generate a gain vector K. The vector K is used in state feedback for altering the poles of the system so as to meet step response requirements such as settling time and percent overshoot. To obtain the gain vector K by the proposed genetic approaches, a pair of ideal, desired poles is calculate first. Those poles serve as the basis by which an initial population is created. In the island approach, those poles serve as a basis for n populations, where n is the dimension of the necessary K vector. Each member of the population is tested for its fitness (the degree to which it matches the criteria). A new population is created each “generation” from the results of the previous iteration, until the criteria are met, or a certain number of generations have passed. Several case studies are provided in this paper to illustrate that this new approach is working, and also to compare performance of the two approaches.